Solve for $x$ and $y$ using elimination. $\begin{align*}-8x-8y &= 1 \\ -x+6y &= -6\end{align*}$
Solution: We can eliminate $y$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $3$ and the bottom equation by $4$ $\begin{align*}-24x-24y &= 3\\ -4x+24y &= -24\end{align*}$ Add the top and bottom equations. $-28x = -21$ Divide both sides by $-28$ and reduce as necessary. $x = \dfrac{3}{4}$ Substitute $\dfrac{3}{4}$ for $x$ in the top equation. $-8( \dfrac{3}{4})-8y = 1$ $-6-8y = 1$ $-8y = 7$ $y = -\dfrac{7}{8}$ The solution is $\enspace x = \dfrac{3}{4}, \enspace y = -\dfrac{7}{8}$.